Let
f(x) = 3x^2 + 2 if x <= 3
f(x) = ax^2 + 2 if x > 3
Find a if the graph of y = f(x) is continuous (which means the graph can be drawn without lifting your pencil from the paper).
It would be nice if the function keeps being 3x^2 + 2 throughout.
Since the graph of y = 3x^2 + 2 is a parabola, we know that it is continuous.
Then a = 3 is the answer.
